-
Heterogeneous household finances and the effectof fiscal
policy∗
Javier Andrésa, José E. Boscáa,b, Javier Ferria,b and Cristina
Fuentes-Alberoc
a University of Valenciab FEDEA
c Federal Reserve Board
February, 2016.
Abstract
This paper analyses the link between fiscal policy,
heterogeneous household finances, andhouseholds’ consumption
response. Our model economy is populated by six types of
householdswith identical labour income, but different balance sheet
composition. We show that heterogeneityin the structure of
household finance is key to understanding the effects of fiscal
shocks. In particular,we conclude that: (1) the marginal propensity
to consume is negatively correlated with net worth;(2) the size of
fiscal effects is positively correlated with wealth inequality; and
(3) the welfare effectsamong heterogeneous households depend
heavily on the composition of net worth.
Keywords: household finances, fiscal policy, heterogeneity.JEL
Classification: E21, E62.
1. IntroductionWealth ownership in many advanced countries has
always been concentrated in the handsof a small minority of the
population. In fact, wealth inequality increased in the
GreatModeration period in the US and other developed countries and
continued to do so duringthe Great Recession. The wealth share of
the U.S.’s top 3 percent (see Federal ReserveBoard Survey of
Consumer Finances, 2014) rose from 44.8 percent of the country’s
wealth
∗ This work was supported by Fundación Rafael del Pino; BBVA
Research; and the Spanish Ministry of Eco-nomy and Competitiveness
(grant ECO2014-53150-R).
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in 1989 to 51.8 percent in 2007 and 54.4 percent in 2013. In the
U.S., wealth held by the top3 percent of the population is twice as
much as that in the hands of the poorest 90 percent.During the
Great Moderation period, this issue received little attention from
economicresearchers, given that, at the same time, consumption
differences across households werereduced. The financial sector was
playing a key role favouring that wealthy people (bigsavers)
provided loans to finance consumption of the less favoured part of
the popula-tion and, thus, reducing the differences in consumption
across households. As a resultconsumption inequality was reduced,
although wealth inequality increased.
However, the financial turmoil in 2008 brought about an
important recompositionof the balance sheets of many households.
The crisis exerted a devastating effect onthe ability of households
to obtain credit and also on the prices of many financial andreal
assets. While the value of private sector assets’, in particular
real state, plummeted,deflation increased the real value of debt.
The subsequent fiscal responses in many coun-tries were thus
carried out against the backdrop of economies with households
charac-terised by very different assets/liabilities positions than
the ones prevailing before thecrisis. For this reason, researchers
and policy makers have made substantial efforts toassess to what
extent fiscal multipliers are now very different from the ones
estimatedbefore the crisis (see e.g. the surveys by Ramey, 2011 and
Spilimbergo et. al., 2009).The most recent economic literature has
gone a step further combining macroeconomicand microeconomic
empirical and theoretical analysis to shed some light on the
linksbetween fiscal policy, heterogeneous household finances and
their consumption responsesto shocks. The main idea of this strand
of the literature consists in using microeconomicdata, coming from
different surveys, to match the stylised facts regarding the
compositionof households finances. This type of approach will allow
a better understanding of thereaction of economies to fiscal and
other kinds of shocks.
In this paper, we carry out a macroeconomic analysis of these
issues within theframework of a general equilibrium model populated
by six types of consumers. House-holds differ in the composition of
their balance sheets. These households’ categories havebeen used
individually, or in different combinations, in many macroeconomic
models de-veloped in the general equilibrium literature.1
Specifically, we identify standard Ricardianoptimising households
(R), typical hand-to-mouth or rule-of-thumb consumers (HNH)that
hold neither assets nor liabilities, wealthy HtM consumers (HH)
that hold assetsbut no liabilities, borrowers with either high or
low capacity to access credit backed bycollateral (BL and BH,
respectively) and, finally, what we call Eggertsson-Krugman typeof
consumers (EK) that do not posses collateralisable assets and
borrow against their future
1 See Eggertsson and Krugman (2012), Gali, López-Salido and
Vallés (2007), Iacoviello (2015), and Andrés,Boscá and Ferri (2015
and 2016).
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labour income.Identifying marginal propensities to consume using
wealth changes is difficult be-
cause individuals differ in labour income, employment status,
productivity, education,etc. Our theoretical model limits the scope
of heterogeneity among households only totheir balance sheet
position. The paper aims to isolate net worth effects of fiscal
shocksand, to that end, we assume perfect insurance to
unemployment. In particular, labourincome is identical across
individuals in a search and matching environment. Thus, after
agovernment expenditure shock, all households in the economy face
the same variation intheir labour income, but idiosyncratic
reactions of their net worth. This framework allowsus to look in
detail at the general equilibrium mechanism underlying the
consumptionreaction to specific net wealth variations of the
various agents in the economy, and in turnto the aggregate
consumption and output effects of fiscal policy.
The model is calibrated to match the most salient features of
the U.S. economy. Weinspect the mechanism considering alternative
theoretical wealth distributions and accessto credit among the
population. We then give the simulated model a more solid
empiricalfoundation by improving the calibration of the model with
the share of these types ofhouseholds identified in the Panel Study
of Income Dynamics (PSID). We identify differenttypes of consumers
that are heterogenous in terms of the composition of their
balancesheets and that match to some extent the features of the
individuals in our theoreticalmodel.
We conclude that matching stylised facts regarding households
finances is key tounderstand the reaction of economies to fiscal
shocks. Our results show that changingthe composition of the
population according to their financial positions has
importanteffects on the aggregate marginal propensity to consume
and the output multiplier. Atthe individual level, the marginal
propensity to consume is negatively related with networth. Model
simulations show that the size of the fiscal effect is positively
correlatedwith wealth inequality. Finally, we compute the effect in
our model of fiscal shocks onhousehold’s welfare, showing that
welfare effects depend heavily on the composition ofnet worth.
Summing up, we conclude that households in the lowest part of
the net wealthdistribution (HH, HNH and EK households in our
economy) can affect importantly themagnitude of the aggregate
marginal propensity to consume, the value of the fiscal multi-plier
and the distributional consequences of fiscal shocks.
Section 2 presents a succinct review of the recent empirical
literature on the macro-economic implications of alternative
household balance sheets. Section 3 introduces themodel and its
calibration. The simulation exercises are presented in Section 4.
Section5 contains a description of the data set, the criteria used
to identify the different house-
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holds’ categories and some additional simulation exercises based
on this data. Section 6concludes.
2. Literature reviewKaplan, Violante and Weidner (2014) use
survey data on household portfolios for the U.S.,Canada, Australia,
the U.K., Germany, France, Italy, and Spain to document the
sharesof the so called hand-to-mouth (HtM) households across
countries, their demographiccharacteristics and the composition of
the assets side of their balance sheets. They identifytwo types of
HtM households: poor hand-to-mouth (with little or no liquid wealth
andno illiquid wealth) and the wealthy hand-to-mouth (with little
or no liquid wealth, butsignificant amounts of illiquid assets).
Using data of the Survey of Consumer Finances forthe U.S., they
conclude that about 30% of the population is HtM, from which
one-thirdis poor HtM and the remainder is wealthy HtM. The authors
find that both wealthy andpoor HtM households have significantly
stronger responses to transitory income shocksthan non-HtM
households. They show that ignoring that wealthy hand-to-mouth can
useilliquid assets to buffer large negative shocks overstates the
overall financial fragility ofHtM households.
In a similar vein, Angrisani, Hurd and Rohwedder (2015) use
panel data spanningthe years 2001-2011 on a complete inventory of
household spending and assets. Theyestimate the response of private
spending to negative wealth shocks in the US due tounexpected
declines in house and stock market prices. Their main finding is
that themarginal propensity to consume out of an unexpected housing
wealth change is sevencents per dollar, and about four cents per
dollar out of financial wealth. So, they find thatconsumption was
reduced in the Great Recession because of losses in housing wealth
andalso, although less precisely estimated, because of financial
wealth losses.
Other authors put the emphasis on the importance of the
composition of the lia-bilities side of the balance sheet of
households to understand the consumption responsesof individuals to
income shocks. For example, Cloyne and Surico (2014) use
householdexpenditure data from 1978 to 2009 of the UK’s Living
Costs and Food Survey (commonlyknown as the Family Expenditure
Survey) to show that households with mortgage debtexhibit large and
persistent consumption responses to changes in their income. In
con-trast, homeowners without a mortgage do not appear to react,
independently of the timehorizon considered.
The references above look either at the assets or the
liabilities side of balance sheets.But both sides of the T-account
are important in shaping the effects of shocks on house-holds’
consumption and, thus, on aggregate output in the economy. Other
papers havealso looked at the net worth, defined as the value of
households’ asset holdings net of
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debt, trying to understand the evolution of consumption over the
recent years. Jaramilloand Chailloux (2015) base their analysis on
an unbalanced panel dataset for 14 advancedeconomies, from 1998 to
2012. They separate the effects on private final
consumptionexpenditure of the subcomponents of disposable income
(labor income, social benefits,personal income taxes and social
security contributions) and of different categories of netwealth
(financial assets, housing assets, and household debt), finding a
significant long-term relation between consumption and the
different components of income and wealth.While labor income
remains the main driver of consumption, financial assets and
housingassets are found to have a positive coefficient, while
household debt has a negative one.Furthermore, these authors’
results suggest that the contribution to consumption from
anincrease in financial or housing assets would be more than offset
if financed fully throughincreases in household debt.
Carroll, Slacalek and Tokuoka (2014) document the importance of
matching sty-lised facts at the household level to interpret the
reaction of economies to shocks. Usingdata from 15 European
countries, they find that wealth inequality and differences in
thedynamics of household income affect the response of economies to
fiscal stimuli in aneconomically relevant way. In their sample they
track down substantial heterogeneity innet wealth to income ratios
both across and within countries. Countries in which house-holds
tend to hold more net wealth respond less strongly to transitory
income shocks,while countries with more unequal wealth
distributions have a higher aggregate marginalpropensity to consume
(MPC) and also a larger dispersion of MPCs across householdsand,
thus, respond more strongly to shocks. Finally, Anderson, Inoue and
Rossi (2015)present empirical evidence based on a narrative
approach, finding that individuals whoseconsumption levels are most
negatively affected by a positive government spending unex-pected
shock are the wealthiest and working-age individuals, whereas
consumption of thepoorest increases the most. Thus, the interesting
conclusion is that positive governmentspending policy shocks tend
to decrease consumption inequality.
Overall, the most important implication of this burgeoning
(mostly) empirical litera-ture is that the net wealth position of
households is a major determinant of their spendingdecisions, and
hence that the distribution of wealth in an economy interacts with
(affectsand is affected by) fiscal policy shocks in a non trivial
manner. This is true not only forthe case of tax changes, whose
incidence on household wealth is more direct, but alsofollowing
changes in public spending, through their macroeconomic effects on
both theasset and the liabilities sides of the balance sheet.
3. The modelThis section presents a stylised version of our
model economy. A complete description of
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the model can be found in the Appendix 1.The economy is
populated by six different types of households, being N the
total
size of the working-age population. Households differ in terms
of some few characte-ristics, as housing tenancy, the degree of
impatience, or the ability to accessing credit.Let Ni denote the
i-type household mass, with i denoting an element of the set I ={R,
HNH, HH, BL, BH, EK}. The meaning of the previous acronyms is as
follows: Rstands for Ricardian households; HNH are hand-to-mouth
households with no access tofinancial markets and no real or
financial assets; HH captures hand-to-mouth householdsthat can
purchase and own houses, but, as for HNH households, total
expenditures areequal to current income every period ; BL
represents households that are able to borrowagainst a low
proportion of the expected value of a collateralised housing asset;
BH standsfor households that are able to collateralise a higher
part of the next-period expectedvalue of their housing; and EK
stands for households that are allowed to borrow againsttheir
future labour income. Define τi = N
i
N (∑i∈I
τi = 1) as the weight of the i-type
household in the total population. For convenience, we also
define different subsets ofhouseholds belonging to I. First, let ĩ
be the index for the households in the subsetĨ = {HNH, HH, BL, BH,
EK} referring to the different households facing a high degreeof
impatientness. Second, define the subset Î = {R, BL, BH, EK} ,
whose elements areindexed by î, as the subset for those households
that have access to financial markets.Finally, consider I = {R, HH,
BL, BH} , indexed by i, as the subset of households that
ownhouses.
Financially unconstrained Ricardian households (R) have been
during a long timethe main character in representative agent
macroeconomic models. These households aretypically savers/lenders
that own assets, but do not have liabilities. In our economy,
Ri-cardian consumers coexist with financially constrained
individuals, who are characterisedby having a higher degree of
impatience. Typical hand-to-mouth consumers (HNH) werepopularised
by Galí, López-Salido and Vallés (2007) to obtain a positive
response of ag-gregate consumption to a government spending shock.
Contrary to Ricardian consumers,these households have no assets,
but also no liabilities, so their net worth is zero. Morerecently,
Kaplan, Violante and Weidner (2014) defined the wealthy
hand-to-mouth house-holds as those that consume all their
disposable income every period but have sizableamounts of wealth in
illiquid assets (this is the role played by our HH households).
BLand BH households are of the type designed by Kiyotaki and Moore
(1997) and Iacoviello(2005). These individuals own both assets and
liabilities and display a positive net wealthin the long run which
is lower the higher the capacity to borrow. The type of
householdsthat are able to borrow against their future labour
income (EK) were used by Eggertssonand Krugman (2012) to illustrate
the power of fiscal policy in highly leveraged economies.
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Compared to Ricardian consumers, these households are located in
the other extremeregarding the composition on their net worth, as
they have only liabilities but no assets.
In order to emphasize the importance of household net wealth
heterogeneity on theeffects of fiscal policy, we assume that all
households in the economy receive the samelabour income. In
particular, we assume that all workers are equally productive
anddelegate to a trade union the negotiation with firms, so that in
equilibrium all of themreceive the same wage, work the same number
of hours and display identical employmentrates.
3.1 Households’ problemThe optimisation problem faced by a
household of type i can be expressed as,
maxcit ,b
ît ,x
it ,d
Rt ,k
Rt ,j
Rt
Et∞
∑t=0(βi)t
[ln(
cit)
+φix ln(
xit)
+nit-1φ1(1-l1t)1−η
1-η+(1-nit-1)φ2
(1-l2)1-η
1-η
](1)
subject to:
cit+jRt
(1+
φ
2
(jRt
kRt−1
))+qt
(xit-x
it−1)= -(1+rnt−1)
(bît-1
1+πt+
dRt-11+πt
)(2)
+rtkRt−1+wtnit−1l1+b
ît+d
Rt + f
Rt +trht
kRt = jRt + (1− δ)kRt−1 (3)
biti∈ Ĩ∩ Î
≤ ϕi[
miEt
(qt+1 (1+ πt+1) xit
1+ rnt
)](4)
+(1− ϕi)[
mEKEt
((1+ πt+1)wt+1nitl1t+1
1+ rnt
)]
nit = (1− σ)nit−1 + ρit(1− nit−1) (5)
Variables in this problem are normalised by the within-group
working-age popula-tion (Nit). The index i in variables and
parameters points to a specific financial structureof the
household. Those with a ĩ superscript refers to the subset of
financial constrainedconsumers, and the ones indexed by R affects
only to consumers from Ricardian house-holds. Non-indexed variables
and parameters are common to all households in the
modeleconomy.
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The meaning of the variables implied in the utility function (1)
is the following:cit, x
it,n
it−1 and (1− nit−1) represent, respectively, consumption,
housing holdings, and the
beginning of period employment and unemployment rates of
different households. Thetime endowment is normalised to one and,
hence, l1t and l2 are an index of hours workedper employee and
hours devoted to job seeking by the unemployed. While there is
aprocess of bargaining over l1t, the amount of time devoted to job
seeking (l2) is assumedto be exogenous and the same among workers.
The discount rate parameter, βi, and thepreferences on housing,
φix, can differ depending on the household class the
consumerbelongs. However, the Frisch elasticity of the labour
supply, related with η, and thevaluation of leisure by employed
(φ1) and unemployed (φ2) workers are assumed to bethe same for all
the agents.
Regarding the budget constraint (2) all consumers earn labour
income wtnit−1l1t,where wt stands for hourly real wages. Latter on
we will comment that under our assump-tions nit−1 = nt−1 for all i
∈ I, so that labour income is homogeneous across all
householdtypes. Also, all consumers receive (pay) the same amount
of lump sum transfers (taxes)from (to) the government (trht). When
trht is negative it is considered a tax. Consumptionis represented
by cit.
Ricardian consumers, who are more patient than the rest of
agents and, thus, arecharacterised by a high value of βi, are the
only lenders in the economy. Ricardians lend inreal terms −bit to
the private sector (implying that bit is negative when i = R) and
−dRt tothe public sector. Debt contracts are set in nominal terms
and they earn an amount −(1+rnt−1)
(bRt−1
1+πt+
dRt−11+πt
)from financial asset holdings, where rnt−1 is the nominal
interest rate
on loans between t− 1 and t. These patient consumers are also
assumed to be the only oneswho own physical capital (kRt ) that
yields rt−1k
Rt−1, where rt represents the gross return on
physical capital. Capital accumulates according to (3), where
jRt stands for productiveinvestment and δ is the depreciation rate.
Investment is subject to increasing marginalcosts of adjustment
which are controlled by the parameter φ. Moreover, given that
firmsmake extraordinary profits, we assume that lenders receive
these in the form of dividendsf Rt .
The rest of consumers in the economy, those belonging to the
subset Ĩ, are assumedto be more impatient than Ricardians and face
the same discount factor, βĩ < βR. From thesubset of impatient
consumers only those belonging to Î have access to credit,
althoughin a restrictive way. These are households of type BL, BH,
EK. Loans have differentconsideration depending on the degree of
securitization. There is debt backed by collateralbut also not
morgaged debt in the economy, and the possibility of access each of
themdepends on the parameter ϕi. We assume that for BL, BH
households ϕi = 1, whichmeans that the total amount of debt they
can get is a fraction of the liquidation value
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of their housing stock. However for the EK consumers we assume
that ϕi = 0 so thatthey can take loans up to a proportion of the
discounted expected tomorrow’s labourincome.2 The impatient
households’ intertemporal substitution is limited as representedby
the corresponding Euler equation in consumption,
λi1ti∈ Ĩ∩ Î
= βiEtλĩ1t+1
(1+ rnt
1+ πt+1
)+ µit (1+ r
nt ) (6)
where µit is the shadow price associated with the constraint
(4).
There is a fixed amount of real estate in the economy and the
term qt(
xit − xit−1)
denotes housing investment, where qt is the real housing
price.The remaining constraint faced by households concerns the law
of motion for em-
ployment. Each period, jobs are destroyed at the exogenous rate
σ. Likewise, new em-ployment opportunities come at the rate ρwt
that represents the probability that one un-employed worker will
find a job, which is taken as exogenous by individual workersbut is
endogenously determined at aggregate level. Actually, ρwt can be
defined as thenumber of matched workers during period t over the
volume of unemployed workers atthe beginning of period t,
ρwt (1− nt−1) = χ1vχ2t [(1− nt−1) l2]
1−χ2 (7)
where vt stands for the number of active vacancies during period
t, being χ1 and χ2 theparameters in the matching function.
For later use we define the marginal value of employment for a
worker (λiht) as,
∂Wit∂nit−1
≡ λiht=λi1twtl1t+(
φ1(1-l1t)1−η
1-η-φ2(1-l2)1−η
1-η
)+ (1-σ-ρwt )β
iEtλiht+1 (8)
where Wi(Ωit) represents the value function of households’
maximum utility. λiht measures
the marginal contribution of a newly created job to the utility
of the household. The firstterm captures the value of the cash-flow
generated by the new job in t, i.e. the labourincome measured
according to its utility value in terms of consumption (λi1t is the
marginalutility of consumption). The second term on the right-hand
side of (8) represents the netutility stemming from the newly
created job. Finally, the third term represents the "capitalvalue"
of an additional employed worker, given that the employment status
will persist inthe future, conditional to the probability that the
new job will not be lost.
2 Alternatively we could have allowed for different types of
loans for all impatient households, with a propor-tion refereing to
mortgaged debt and the rest being just backed by expected labor
income. We find our modelingchoice easier to handle without much
loss of accuracy in the exercises berlow.
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3.2 Firms’ problemFor convenience, production is organised in
three different levels: (1) a wholesale sector(indexed by j) where
firms use labour and capital to produce a homogenous good thatis
sold in a competitive flexible price market at a price Pwt ; (2) an
intermediate sectorwhose firms (indexed by j̃) operates in a
monopolistically competitive fashion in whichprices are sticky.
These firms buy the homogenous good and transform it, without
theuse of any other input, into a firm-specific variety; (3) a
competitive retail aggregator thatbuys differentiated varieties (y
j̃t) from the intermediate sector at a price P̃jt and sells
ahomogeneous final good (yt) at price Pt.
The competitive retail sector
The competitive retail aggregator buys differentiated goods from
firms in the intermediatesector and sells a homogeneous final good
yt at price Pt. Each variety y j̃t is purchased at aprice P̃jt.
Profit maximisation by the retailer implies
Maxy j̃t
{Ptyt −
∫P̃jty j̃td j̃
}subject to,
yt =[∫
y(1−1/θ)j̃t
d j̃
] θθ−1
(9)
where θ > 1 is a parameter that can be expressed in terms of
the elasticity of substitutionbetween intermediate goods (κ), as θ
= (1+κ) /κ. The retailer’s price is given by:
Pt =[∫ 1
0
(P̃jt)1−θ
dj̃] 1
1−θ(10)
The monopolistically competitive intermediate sector
The monopolistically competitive intermediate sector comprises
j̃ = 1, ... J̃ firms, each ofwhich buys the production of
competitive wholesale firms at a common price Pwt and sellsa
differentiated variety y j̃t at price P̃jt to the final competitive
retailing sector describedabove. Variety producers stagger prices.
In keeping with Calvo (1983), only some firmsset their prices
optimally each period. Those firms that do not reset their prices
optimallyat t adjust them according to a simple indexation rule to
catch up with lagged inflation.Thus, each period a proportion ω of
firms simply set P̃jt = (1+ πt−1)
ς P̃jt−1 (with ςrepresenting the degree of indexation and πt−1
the inflation rate in t− 1). The fraction of
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firms (of measure 1−ω) that set the optimal price at t seek to
maximise the present valueof expected profits. Consequently, 1−ω
represents the probability of adjusting prices eachperiod, where ω
can be interpreted as a measure of price rigidity. The solution to
choice ofthe optimal price for the representative variety producer
is
P∗t =(
θ
θ-1
) Et ∑∞s=0 (βRω)s λR1t+s[
mct+s (Pt+s)θ yt+s
(s
∏s′=0
(1+πt+s′-1)ς)-θ]
Et ∑∞s=0(
βRω)s
λR1t+s
[(Pt+s)
θ-1 yt+s
(s
∏s′=0
(1+πt+s′-1)ς)1-θ] (11)
where P∗t is the price set by the representative optimizing firm
at time t, and mctrepresents the real marginal cost. In accordance
with the ownership structure of the eco-
nomy, future profits are discounted at the relevant
rate((βR)s
λR1t+sλR1t
)of the patient house-
hold.Taking into account (10) and that θ is assumed time
invariant, the corresponding
aggregate price level is given by,
Pt =[ω(
Pt−1πςt−1)1−θ
+ (1−ω) (P∗t )1−θ] 1
1−θ (12)
The competitive wholesale sector
The competitive wholesale sector consists of j = 1, ...J firms,
each selling a different quan-tity of a homogeneous good at the
same price Pwt to the monopolistically competitiveintermediate
sector. Firms in the perfectly competitive wholesale sector carry
out theactual production using labour and capital. Capital demand
and vacancy posting aredecided by solving the cost minimisation
problem faced by the representative competitiveproducer,
minkt ,vt
Et∞
∑t=0(βR)t
λR1t+1
λR1t(rt−1kt−1 + wtnt−1l1t + κvvt) (13)
subject to the production function
yt = Ak1−αt−1 (nt−1l1t)α (14)
and the law of motion for employment
nt = (1− σ)nt−1 + ρft vt (15)
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From the firms’ point of view, labour is homogeneous regardless
of the type of householdthat provides it and ρ ft is the
probability that a vacancy will be filled in any given periodt. The
probability of filling a vacant post ρ ft is exogenous from the
perspective of the firm.However, as far as the overall economy is
concerned, this probability is endogenouslydetermined according to
the following Cobb-Douglas matching function:
ρft vt = χ1v
χ2t [(1− nt−1) l2]
1−χ2 (16)
The solution to the optimisation program above generates the
following first-orderconditions for private capital and the number
of vacancies
rt = (1− α)mct+1yt+1
kt(17)
κv
ρft
= βlEtλl1t+1
λl1t
∂Vt+1∂nt
(18)
Expression (18) reflects that firms choose the number of
vacancies in such a way that themarginal recruiting cost per
vacancy, κv, is equal to the expected present value of opening
the vacancy βREtλR1t+1
λR1tρ
ft
∂Vt+1∂nt+1
, where ∂Vt∂nt represents the next period marginal value of
an
additional job that is defined as
λ f t ≡∂Vt
∂nt−1= αmct
ytnt−1
− wtl1t + (1− σ)βlEtλl1t+1
λl1t
∂V ft+1∂nt
(19)
where the marginal contribution of a new job to profits equals
the marginal product net ofthe wage rate, plus the capital value of
the new job in t, corrected for the probability thatthe job will
continue in the future.
3.3 Trade in the labour market: the labour contractWe assume, as
in Boscá et al. (2011), that although households’ types may differ
in theirreservation wages, they delegate wage and hour bargaining
to a trade union. This tradeunion maximises the aggregate marginal
value of employment for workers and distributesemployment according
to their shares in the working-age population. Thus, all
workersreceive the same wage, work the same number of hours and
have the same unemploymentrates.
Following standard practice, the Nash bargaining process
maximises the weighted
-
13
product of the parties’ surpluses from employment.
maxwt,l1t
(∑i∈I
τiλihtλi1t
)λw (λ f t
)1−λw= max
wt,l1t(λht)
λw(
λ f t
)1−λw(20)
where λw ∈ [0, 1] reflects workers’ bargaining power. The term
λht represents the averageworker’s surplus, whereas the term λ f t
is the firm’s surplus. More specifically, λ
iht/λ
i1t de-
note the earning premium (in terms of consumption) of employment
over unemploymentfor a type-i household, respectively. Solving the
Nash maximisation problem we get theoptimal real wage and hours
worked
wtl1t = λw[
mctαyt
nt−1+
κvvt(1− nt−1)
]+(1− λw)
[(φ2(1− l2)1−η
1− η − φ1(1− l1t)1−η
1− η
)∑i∈I
τi
λi1t
]
+(1− λw)(1− σ− ρwt ) ∑ĩ∈ Ĩ
τiEtλĩht+1
λĩ1t+1
(βR
λR1t+1
λR1t− βĩ λ
ĩ1t+1
λĩ1t
)(21)
mctαyt
nt−1l1t= φ1(1− l1t)−η ∑
i∈I
τi
λi1t(22)
3.4 Policy instruments and resources constraintWe assume the
existence of a central bank that follows a Taylor’s rule,
1+ rnt =(1+ rnt−1
)rR ((1+ πt)1+rπ (yty)ry
(1+ rn))1−rR
(23)
where y and rn are steady-state levels of output and interest
rate, respectively. The para-meter rR captures the extent of
interest rate inertia, and rπ and ry represent the weightsgiven to
inflation and output objectives.
Revenues and expenditures are made consistent by means of the
government in-tertemporal budget constraint:
bpt = gt + trht +(1+ rnt−1)
1+ πtbpt−1 (24)
In order to make the debt to GDP ratio stationary, the following
fiscal policy reactionfunction is imposed:
-
14
trht = trht−1 − ψ1
[bt
gdpt−(
bgdp
)]− ψ2
[bt
gdpt− bt−1
gdpt−1
](25)
where ψ1 > 0 captures the speed of adjustment from the
current ratio towards the desired
target(
bgdp
). The value of ψ2 > 0 is chosen to ensure a smooth
adjustment of current debt
towards its steady-state level.Finally, the aggregate resource
constraint guarantees that the sum of demand com-
ponents plus the cost of posting vacancies be equal to aggregate
output,
yt = Atk1−αt−1 (nt−1l1t)α = ct + jt
(1+
φ
2
(jt
kt−1
))+ gt + κvvt (26)
3.5 CalibrationThe calibration strategy for our benchmark model
consists in using standard values inthe literature for some
parameters and matching some relevant data moments for the
USeconomy. In Table 1 we present the values of those parameters
that allow us to identifythe six different types of households that
populate our benchmark economy. Thus, firstwe define the shares of
the households’ categories in the total population, assuming
thatRicardian households represent 50 percent of the population (τR
= 0.5) and the otherfive type of individuals amount each to 10
percent of it (τHNH = τHH = τBL = τBH =τEK = 0.1). The subjective
intertemporal discount rate of patient households is βR =0.99,
while all other five types are more impatient, presenting a
discount factor of 0.95(see Iacoviello, 2005). All individuals that
own houses in our economy share the samepreferences parameter on
housing, φix = 0.12. This value, as well as the the total stockof
housing, X, depend on the value we assign to the ratio of assets of
patient households(b
R) to total output (y) in the steady state, that we set
following also Iacoviello (2005) such
that the total stock of housing over yearly output is 140
percent. Finally, ϕi is set to onefor BL and BH households,
indicating that these individuals take credit using housing
ascollateral, and to zero for EK individuals, indicating that they
borrow against their futurelabour income. Loan-to-value ratios are
set to 0.735 (for BL households) and 0.985 (for BHand EK
individuals), values that are slightly lower and higher than those
in Iacoviello andNeri (2010).
The remaining set of parameters is shown in Table 2. We take
very standard valuesfor the Cobb-Douglas parameter α = 0.7 and the
depreciation rate of physical capitalδ = 0.025. The elasticity of
matching to vacant posts χ2 = 0.5 comes from Monacelliet al (2010),
whereas the exogenous transition rate from employment to
unemployment,
-
15
Table 1. Parameterization of householsType τi β φix ϕ
i mi
R 0.5 0.99 0.12 −− −−HNH 0.1 0.95 0 −− −−HH 0.1 0.95 0.12 −−
−−BL 0.1 0.95 0.12 1 0.735BH 0.1 0.95 0.12 1 0.985EK 0.1 0.95 0 0
0.985
σ = 0.15, is taken from Andolfatto (1996) and Cheron and Langot
(2004). These authorsalso provide some average steady-state values,
such as the probability of a vacant positionbecoming a productive
job, which is assumed to be ρ f = 0.9, the fraction of time
spentworking, l1 = 1/3, and the fraction of time households spend
searching l2 = 1/6. Thelong-run employment ratio is computed to be
n = 0.75 as in Choi and Rios-Rull (2008).Furthermore, we assume
that equilibrium unemployment is socially-efficient (see
Hosios,1990) and, as such, λw = 0.5 is equal to 1− χ2. For the
intertemporal labour elasticity ofsubstitution, we consider η = 2
implying that average individual labour supply elasticity(
η−1(
1/l1 − 1))
is equal to 1, the same as in Andolfatto (1996). The adjustment
costsparameter for productive investment φ = 5.5, is taken from
QUEST II, which considers thesame function as ours for capital
installation costs. Parameters affecting the New PhillipsCurve are
also standard in the literature. We set a value of θ = 6 for the
elasticity offinal goods implying a steady state markup of θθ−1 =
1.2. Hence, the steady state valuefor the marginal cost is obtained
as mc = θ−1θ . The probability of not changing prices,ω, is set to
0.75, meaning that prices change every four quarters on average,
whereas wetake an intermediate value, ς = 0.4, for inflation
indexation. Regarding Taylor’s rule, theparameters rR = 0.73 and rπ
= 0.27 are taken from Iacoviello (2005). We choose a value of0, for
the parameter measuring the interest rate reaction to output
ry.
We normalise both steady-state output (y) and real housing
prices (q) to one. Steady-state government expenditure g/y, is set
to 17 per cent of output, matching US data. Weobtain the long-run
value for vacancies from (19) v = σn/ρ f . Then, we calibrate the
ratioof recruiting expenditures to output (κvv/y) to represent 0.5
percentage points of output,as in Cheron and Langot (2004) or Choi
and Rios-Rull (2008), and very close to the value of0.44 implied by
the calibration of Monacelli et al. (2010). From this ratio we
obtain a valueof κv = 0.04 and using the steady-state version of
the equation (18), we can solve for thevalue of wages (w). The
steady-state value of matching flows in the economy equals theflow
of jobs that are lost (σn) and we use the equality (σn = χ1v
χ2 [(1− n) l2]1−χ2 ) to solvefor the scale parameter of the
matching function χ1 = 1.56.
The long-run value of total factor productivity, A = 1.50, is
calibrated from the
-
16
Table 2. Parameter valuesPreferences:Labour elasticity, η
2Leisure preference (empl.), φ1 1.59 Leisure preference (unempl.),
φ2 1.04Technology:Labour share in production, α 0.7 Depreciation
rate of capital, δ 0.025Elasticity of final goods, θ 6 Entry fixed
cost, κ f 0.167Frictions:Probability of not changing prices, ω 0.75
Investment adjustment costs, φ 5.5Inflation indexation, ς 0.4Labour
market:Matching elasticity, χ2 0.5 Transition rate, σ 0.15Workers’
bargaining power, λw 0.5 Cost of vacancy posting, κv 0.04Scale
parameter matching, χ1 1.56Policy:Fiscal reaction parameter, ψ1
0.01 Fiscal reaction parameter, ψ2 0.2Interest rate smoothing, rR
0.73 Interest rate reaction, rπ 0.27Interest rate reaction, ry
0
production function to obtain the steady-state value of Tobin’s
q ratio, λl2
λl1. The return
on capital (r) comes from the first-order conditions and the
steady-state value for capitalstock (k) from (17). Capital stock,
together with the depreciation rate and the adjustmentcost
parameter, allows us to calculate the value of gross investment for
the steady stateand, using the aggregate constraint, the level of
consumption c. The steady-state valueof the nominal interest rate
rn, is related to the intertemporal discount rate of
Ricardianhouseholds through the steady-state version of the
first-order condition for consumption.The value for the lump-sum
transfers in the steady state is such that from the
governmentbudget constraint the resulting debt-to-output ratio is
93 per cent on annual terms. Inorder to compute κ f , we use the
following equality between the source of income andaggregate
spending
c+ j(
1+ δφ
2
)+ gt = nwl + rk+ κ f
where κ f =(
1− τb)
dR.Steady-state levels of the marginal utilities of consumption
of the different types
of consumers, λR1 , λ
HNH1 , λ
HH1 , λ
BL1 , λ
BH1 , and λ
EK1 come from their respective first-order
conditions. As regards leisure preference parameters in the
household utility function,φ1 = 1.59 is calculated from the
steady-state version of expression (22). A system of sevenequations
implying the steady state of expressions (8) for the six categories
of individualsand (21) is solved for φ2, λ
Rh , λ
HNHh , λ
HHh , λ
BLh , λ
BHh , and λ
EKh . The resulting value for φ2 is
-
17
1.04. Therefore the calibrated values for φ1 and φ2 imply that
the value attributed to leisureby an employed worker is well above
that attributed by an unemployed worker.
4. Simulation results
4.1 The distribution of net wealth across householdsTable 3
presents steady state levels of consumption, labour income and net
wealth (andits distribution between assets and liabilities) across
all six household categories in oureconomy. The model assumptions
on the labour market warrant the same labour incomeacross all
household types (second column of Table 3) so that, as Table 3
shows, there is avery unequal steady state distribution of net
wealth but a more egalitarian distribution ofconsumption.
Ricardian consumers own the bulk of assets and most net wealth
in the economy,with a ratio of net worth over labour income close
to sixty. This is not surprising, as inour model these households
are the only ones that save, provide credit funds and own
allproductive capital. But net wealth is also very different among
those household types thatare subject to some kind of borrowing
constraint, depending on the composition of theirbalance sheets. In
particular, and focusing on assets and liabilities holdings, we
covera wide range of combinations that range from households with
assets and no liabilities(our R households or Ricardian consumers)
to the Eggerstsson and Krugman householdstype with liabilities and
no assets (our EK households), through consumers with neitherassets
nor liabilities (our HH or RoT households), or those households
that hold assetsand liabilities in different proportions depending
on their easiness of access to credit (ourBL and BH or the
Iacoviello type households). Also, although our HH consumers
sharewith Ricardians a positive net worth, given that both do not
hold liabilities, they differin their inability to smooth
consumption over time, so that they exhaust all their incomeevery
period. Thus, although the wealthy-hand-to-mouth individuals of
Kaplan et al.(2014), hold presumably much more total wealth than
our HH households, the fact thatthey chose to save most of that
wealth in highly illiquid assets, clearly differentiates
theirpattern of consumption with respect to Ricardian
consumers.
Overall, the picture that arises from Table 3 with respect to
the distribution of networth and labour income, summarised in the
last column of the table (representing theratio of net wealth over
labour income), is in line with empirical estimates by Carrollet
al. (2014). These authors use data from the European Household
Finance and Con-sumption Survey to show substantial heterogeneity
in wealth-to-permanent income ratios,both across and within
countries. Regarding the steady state levels of consumption
across
-
18
Table 3. Steady state consumption, labour income and net
wealthCons Lab income Net wealth Assets Liabilities Ratio
(1) (2) (3) (4) (5) (3)/(2)R 0.760 0.578 33.104 33.104 0 57.3HNH
0.557 0.578 0 0 0 0HH 0.557 0.578 1.344 1.344 0 2.3BL 0.534 0.578
0.829 3.128 2.299 1.4BH 0.501 0.578 0.085 5.702 5.616 0.15EK 0.551
0.578 -0.569 0 0.569 -0.98
agents, presented in column 1 of the table, not surprisingly
Ricardian consumers displaythe highest levels of per capita
consumption across households, since they hold most assetsin the
economy and have no liabilities.
Both types of hand-to-mouth consumers are the ones who achieve
the highest con-sumption levels among the restricted household
types in our setting. This is so, becausein the steady state they
consume all their labour income and, given that they do not
haveliabilities on their balance sheets, they do not need to make
any interest rate payments(notice also that in the steady state
there is no housing investment, so HH consumers donot spend on
housing). Finally, among the household types that participate in
the creditmarket per capita consumption levels are inversely
related with the amount of liabilitiesthey hold. Thus, EK consumers
consume more than borrowers with a low capacity toget credit, and
these more than the ones with easy access to loans. In the steady
stateindebted households have to distribute their incomes between
consumption and debtinterest payments. So, given equal labour
incomes, heavily indebted households will reachlower consumption
levels.
4.2 Consumption dynamicsIn this subsection, we analyze the role
played by household balance-sheet heterogeneityin shaping the
short-run response of consumption to a transitory government
spendingshock. Figure (1) shows the impulse response functions of
output and consumption forthe benchmark parameterization. Upon
impact, the response of output to a 1% increaseis government
spending is larger than 1%. Therefore, the output multiplier is
largerthan 1. The government spending shock generates a crowding-in
effect in consumption.This aggregate response of consumption,
however, hides a very heterogeneous reaction ofconsumption and net
wealth for the different households. The extreme cases are: (i)
theconsumption by EK households increases by about 4% upon impact
and (ii) the consump-tion by Ricardian households declines upon
impact.
Figure (2) shows the response of consumption (with respect to
its steady state),labor income, and net worth for each type of
household. Consumption is a function
-
19
2 4 6 8-1
0
1
2
3
4
5Consumption
BL
BH
RH
RNH
EK
O
2 4 6 8-15
-10
-5
0
5Net Wealth
BL
BH
RH
EK
O
2 4 6 8-0.5
0
0.5
1
1.5Output and Consumption
C
Y
Figure 1: Impulse-response to a 1 percent GDP increase in
government spending (relative variation)
of labour income and net worth. As the movement of labour income
is the same allacross households, the response of net wealth
becomes central to understand differentconsumption multipliers.
Ricardian households are affected by the deterioration in their
net worth causedby the fall of the price of real state and
productive capital. The fact that debt contractsare set in nominal
terms reinforces the negative wealth effect as the real value of
debt(
bît−11+πt
+dRt−1
1+πt
)is eroded as a consequence of the rise in current inflation πt.
Although
labour income increases after the shock, the fall in the value
of the large amount of wealthheld by Ricardians consumers
dominates, causing a downward adjustment in their spen-ding.
Turning now to the other households categories, their total
spending capacity de-pends on current labour income, net wealth and
the new credit flow. From (2), totalspending capacity can be
rewritten as:
cit + qtxit = b
it︸︷︷︸
new credit flow
+ qtxit−1 − (1+ rnt−1)bit−1
1+ πt︸ ︷︷ ︸net financial wealth
+ wtl1tnt−1︸ ︷︷ ︸++ trhtcurrent labour income
(27)
Net wealth also falls for households BL and BH due basically to
the downward movementof the price of housing qt, the only asset
available for them. However, this effect is partiallycompensated by
a debt deflation induced by the rise in inflation, which affects
negatively
the termbit−1
1+πt. The effect on net financial wealth is negative but less
pronounced for
-
20
2 4 6 8-10
-8
-6
-4
-2
0
2
Periods
R
ConsumptionIncomeNet Wealth
2 4 6 8-1
-0.5
0
0.5
1
1.5
2BL
2 4 6 8-1
-0.5
0
0.5
1
1.5
2BH
2 4 6 8-1
-0.5
0
0.5
1
1.5
2HH
2 4 6 8-0.5
0
0.5
1
1.5
2HNH
2 4 6 8-0.5
0
0.5
1
1.5
2
2.5EK
Figure 2: Response of consumption by household type to a 1
percent GDP increasein government spending (per capita absolute
variation)
lowly leveraged borrowers. Actually, although BL households are
less leveraged than BHhouseholds (bBLt−1 < b
BLt−1), so that the Fisher effect has less punch on real debt
for them,
they also demand less housing (xBLt−1 < xBHt−1), implying
that the fall in qt has a weaker
effect on lowly indebted households. Considering just the
response of labour income andnet financial wealth, we would expect
a more muted response of consumption for BHthan for BL households.
However, Figure (2) shows the oppositve. The explanation forthis
result relies in the new credit flow term, bit, that responds very
differently for indebtedconsumers. The fiscal shock increases the
expected value of the collateral (Etqt+1xbt ) andreduces the real
interest rate in t, (1+r
nt )
1+πet+1, which according to (4) facilitates the access to
credit. This effect is stronger for BH household since they have
a higher loan-to-valueratio mb.
For EK households, the term qtxit−1 is absent from the spending
restriction. Thus,they do not suffer the drop in the value of
assets, but still they take advantage of theerosion of their real
outstanding debt which makes net wealth to jump initially.
Also,they can easily call for more credit because the increase in
the expected tomorrow’s labourincome. As a consequence, these
households are the ones with a stronger response ofconsumption on
impact.
-
21
Households HH and HNH do not have access to credit, so they
cannot accumulate
debt so the terms bit andbit−1
1+πtdo not appear as consumption drivers in the equation
above. A typical hand-to-mouth consumer, as it has been
considered in the literature,does not possess assets, so for HNH
households terms qtxHNHt and qtx
HNHt−1 disappear
and consumption replicates the evolution of current income,
which stimulate a sizableresponse in the first period. Wealthy
hand-to-mouth households (HH) suffer the decline inthe value of
their assets with no compensation by the other side of their
balance sheet and,hence, their consumption response is the lowest
one among the financially constrainedhouseholds.
4.3 Marginal propensities to consumeFrom expression (27), we can
obtain the different sources for the marginal propensity toconsume
out of labour income (MPC) as,
∆cit∆labit
= 1+∆bit
∆labit+
∆nwit∆labit
−∆(qtxit
)∆labit
(28)
where nwt is the term qtxit−1− (1+ rnt−1)bit−1
1+πtrepresenting the financial net wealth and labit
is the current income. From expression (28), we conclude that
the change in consumptionin response to the change in current
income induced by the shock will be 1 for a householdwith no access
to fresh credit, no net worth and no houses (our HNH households).
How-ever, for the other categories of households the marginal
propensity to consume dependson the induced effect that the change
in labour income produces on new debt, net wealthand housing
investment. Table 4 quantifies the importance of the sources behind
the MPCfor each type of household.
A first conclusion from Table 4 is the large heterogeneity
across households in theconsumption expenditure response to the
increase in labour income induced by the shock.We have ordered
households according to their initial wealth, so that comparing the
firstand the last column we see a clear negative relationship
between the marginal propensityto consume, out of current labour
income, and the wealth of the household. Householdswith less wealth
respond more strongly to an increase in (government spending
induced)income, a result which is consistent with some recent
empirical linking wealth and con-sumption (Carroll et al., 2014;
Kaplan et al., 2014; Angrisani et al, 2015). The centralcolumns
actually corroborate that balance sheets are pivotal in the
distinct reaction ofhousehold consumption, an idea that has already
been documented empirically by Parkeret al, 2013; Agarwal and Qian,
2014; Acconcia et al., 2015; Sahm et al., 2015; Surico andTrezzi,
2015.
-
22
Table 4. Sources of the marginal propensities to consume out of
current income
∆cit∆labit
∆nwit∆labit
∆bit∆labit
∆(qtxit)∆labit
NW − SSR -0.1471 -2.2722 -1.2680 -3.5491 33.104HH 0.0540 -0.2867
– 0.6593 1.344BL 0.0892 -0.3756 1.4106 1.9458 0.829BH 0.3336
-0.5039 5.8540 6.0165 0.085HNH 1.0000 – – – 0EK 1.1556 0.0722
0.0837 – -0.569
In our model, the negative response of Ricardian households’
consumption is mostlydriven by the drop in net worth, whereas the
intense fall in housing investment preventsconsumption spending to
go down by more. On the other extreme the net worth multiplierto
labour income is not large for EK consumers, but in this case its
effect on consumptionis reinforced by the additional credit that
the increase in expected income makes available.Fresh credit is the
main driver explaining the differences between BL and BH
consumers’spending decisions. Also, a comparison between the two
categories of hand-to-mouthhouseholds (RoTs, HNH, and wealthy
hand-to-mouth, HH) makes clear the two channelspulling down the MPC
of HH households: declining wealth and, more importantly,
diver-sion of spending towards additional housing.
4.4 Fiscal multipliers
The distinctive reaction of household consumption induced by the
government spendinggenerates a clear correlation pattern linking
the composition of the population and theaggregate output
multiplier. In Table 5, we calculate the output and consumption
im-pact multiplier to a fiscal shock under different scenarios
regarding the distribution ofhouseholds among the six types
considered. In the first row we assume an economypopulated entirely
by a representative Ricardian consumer. The government spending
in-crease triggers the standard crowding out effect in consumption
and an output multiplierlower than one. In the following rows we
keep the share of Ricardian in a 50 percent anddistribute the
remaining 50 percent equally among the different types of non
Ricardianconsumers in a sequential way. For example, the second row
population is split on equalproportions between Ricardian and HH
households, whilst in the last row the differentclass of non
Ricardian households represent each a 10 percent of the total
population. Theparticular sequence we have chosen for this exercise
implies a continuos change in thesize of the multiplier as we are
adding new households categories to the economy. Thisexercise
offers a rough indicator of what we miss in terms of the effect of
fiscal policy bynot providing enough detail on the households’
side. Overall, the output multiplier to agovernment spending shock
augments by more than 50 percent if we compare the result
-
23
Table 5. Fiscal multipliers∆yt∆gt
∆ct∆gt
R 0.805 -0.205R+HH 0.851 -0.147R+HH+BL 0.874 -0.099R+HH+BL+BH
0.978 0.044R+HH+BL+BH+RNH 1.078 0.166R+HH+BL+BH+RNH+EK 1.224
0.344
of a representative Ricardian household economy to that from an
economy with a sensibledistribution of a wide variety of household
categories.
4.5 Wealth inequality and the fiscal multiplierWe can also
derive from our model some implications regarding the relationship
betweenwealth inequality and the fiscal multiplier. This relates to
the work of Carroll et al. (2014)who postulate a positive
association between wealth inequality and the aggregate MPC.We
explore this issue in Figure (3) plotting the impact output
multiplier against a Ginicoefficient representing different
scenarios about the distribution of households’ categoriesin total
population. In particular, we start by representing the Gini
coefficient and theaggregate output multiplier corresponding to the
benchmark calibration (the Bench pointin the figure) and proceed as
follows: we increase τHH for HH households from 0.1 to0.2 and
reduce correspondingly τR for the Ricardians from 0.5 to 0.4, and
then computefor this new distribution the Gini coefficient and the
output multiplier (point HH in theFigure (3)). We repeat the same
exercise for the rest of households in our model.
The results establish a clear association between the output
multiplier and wealthdispersion. Fiscal policy in a more unequal
economy would display larger effects in termsof output, as the
positive slope in regression line indicates. This relationship is
no morethan the reflection of the heterogeneity in the MPC that we
have explained in Table 4.
4.6 Welfare effectsThe heterogeneity in our model allows us to
compare the effect of a government spen-ding change on the
consumption response across households categories. But
households’utility also depends on their real state holdings. To
assess the distributional consequencesof the policy in a more
global way we compute its effect on household’s welfare. Wedefine
welfare Vi as the discounted sum of a household i period utility,
conditional onthe economy being at the steady state in period 0
(common to all the experiments) and
-
24
Figure 3: Simulated fical multiplier for different distributions
of wealth
remaining constant throughout
Vi =∞
∑t=0(βi)t
ln(cit)+ φix ln(xit)+ nt−1φ1 (1−l1t)1−η1−η+(1− nt−1)φ2
(1−l2)1−η1−η
,
where i is the index referring to household’s type. Now, we
define Vi,s as the welfare of ahousehold of type i under a shock,
conditional on the state of the economy in period t = 0and taking
into account the reaction of the variables before returning again
to their initialsteady state
Vi,s =∞
∑t=0(βi)t
ln(ci,st )+ φix ln(xi,st )+ nst−1φ1 (1−ls1t)1−η1−η+(1−
nst−1)φ2
(1−l2)1−η1−η
, (29)
where ci,st , xi,st , n
st−1 and l
s1t denote consumption, housing, employment rate and hours
per
worker, respectively, under a fiscal shock. We calculate the
welfare cost ∆i associated witha fiscal measure as the fraction of
steady state consumption that a household would be
-
25
Figure 4: Welfare effects by household category
willing to give up in order to be as well off after the fiscal
shock. That is,
Vi,s =∞
∑t=0(βi)t
ln [cit (1− ∆i)]+ φix ln(xit)+ nt−1φ1 (1−l1t)1−η1−η+(1−
nt−1)φ2
(1−l2)1−η1−η
. (30)Thus, from (29) and (30):
∆i = 1− exp{(
Vi,s −Vi) (
1− βi)} (31)
where a negative value for ∆ implies a welfare gain.Figure (4)
shows that the effect in terms of welfare derived from the increase
in
government spending in our model is actually very heterogeneous
among households.There is a drop in aggregate welfare that affects
basically Ricardians and borrowers withhouse tenure (much more to
BH households than to BL households). Wealthy and poorhand-to-mouth
(HH and HNH households) and Eggertsson-Krugman type households,on
the contrary, improve slightly as a consequence of the measure. The
main messagearising from this result is that, besides targeting a
short run effect on output, standardfiscal policy, even under the
assumption that it does not affect preferences, can also beseen as
generating a non negligible distributional response. The way in
which householdspecific welfare is affected depends very much on
her position in the financial market,which determines to a great
extent their balance sheets. It is also important to qualify
the
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26
effects of fiscal consolidations given that our results suggest
that they can benefit the mostthe wealthiest part of the
population.
5. Looking at the dataGiven the relative role played by
household heterogeneity in quantifying fiscal effects,we turn to
micro data in oder to estimate the fraction of U.S. households
belonging toeach of the categories we establish in our theoretical
model. The PSID contains detailedinformation on income,
consumption, and wealth at the household level starting fromthe
1999 wave. The survey is conducted in a biannual basis. Our sample
has 55, 105observations over the pooled years 1999− 2013. Following
Kaplan, Violante and Weidner(2014), we classify households in terms
of their wealth. Let lnwit be the net wealth ofhousehold i defined
as the value of checking accounts, saving accounts, money
marketfunds, certificates of deposits, savings bonds, Treasury
Bills, other IRAs; the value ofprivate annuities or IRAs; the value
of other investment in trusts or estates, bond funds,life insurance
policies, special collections; the net value of farm or business
assets; the netvalue of real estate other than main home; the net
value of vehicles; and the value of debtsother than mortgages.
Therefore, our measure of wealth abstracts from real estate
assetsconsidered as the main home and mortgage debt. Let incit be
the income of household idefined as salaries and other compensation
plus private and government transfers.
Table 6. Identification criterion for PSID dataHousehold Wealth
Homeowner High LTV Low LTV No Mortgage
R lnwit ≥ 0.5 ∗ incit ? ? ? ?BH lnwit ≤ 0 X X x xBL lnwit ≤ 0 X
x X xEK lnwit ≤ 0 x x x xHH 0 < lnwit < 0.5 ∗ incit X x x
X
HNH 0 < lnwit < 0.5 ∗ incit x x x xNOTES: incit stands for
wealth and lnw
it for income.
Our identification strategy is described in Table 6. Ricardian
households are thosewhose average liquid wealth balances are
positive and equal to or more than half of theirincome. Following
Kaplan, Violante and Weidner (2014), half of the earnings per
pay-period is due to the assumption that resources are consumed at
a constant rate. Wedo not impose any additional constraint to
identify Ricardian households, that is, theymay or may not be
homeowners and they may or may not have a mortgage. Hand-to-mouth
consumers, both poor and wealthy, are assumed to have positive
wealth balances
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27
Table 7. Sample Weights (in %) in PSID1999 2001 2003 2005 2007
2009 2011 2013
R 50 50 49 48 48 43 42 41BH 5 6 7 7 7 8 7 7BL 3 3 3 3 3 3 3 3EK
17 17 17 18 19 23 24 24HH 5 4 5 4 4 3 4 4
HNH 20 20 19 19 20 20 20 21Total obs 5,836 6,134 6,504 6,677
7,037 7,342 7,661 7,914
but these are less than half their earnings. Wealthy
hand-to-mouth households, HH,are homeowners, therefore they hold
illiquid wealth, but do not have mortgage debtoutstanding. Poor
hand-to-mouth households, HNH, are restricted to not be
homeownersnor having mortgage debt outstanding. The remaining three
categories of households,borrowers with high loan-to-value (LTV
hereafter) ratio, BH, borrowers with low LTVratio, BL, and
Eggerston-Krugman households, EK, are assumed to hold negative
liquidwealth balances. While EK households do not hold real estate
nor mortgage debt, BHand BL households are homeowners and have
mortgage debt outstanding. We classify ahousehold as BH if her LTV
ratio is equal to or larger than the average LTV in the
sampleperiod.
We report the sample weights for each type of households in
Table 7. Overall, thedistribution of household types is fairly
stable with a notable exception: over time, thefraction of
Ricardian households in the U.S. economy has declined from 50% in
1999 to41% in 2013, with the proportion of EK households increasing
in parallel from 17% to24%. We feed the model with the estimated
weights from the PSID data and compute thefiscal multiplier. Table
8 reports the evolution of the multiplier. In the years prior to
theGreat Recession, the fiscal multiplier remains fairly stable.
The fiscal multiplier increasessignificantly whenever the relative
weight of Ricardian households and EK householdschanges. The
response of consumption by EK households to a fiscal shock was the
largestin our baseline calibration, while the response of Ricardian
households was negative.Therefore, it is not surprising that the
size of the fiscal multiplier increases when the shareof Ricardians
drops or the share of EK households increases. Overall, between
2005 and2013 the multiplier grows more than 30 per cent.
6. Concluding remarksWe have introduced an otherwise standard
New Keynesian DSGE augmented to allowfor some degree of
heterogeneity in the population. More specifically we focus on
thepresence of individuals with different connections with the
financial market, that generateheterogeneity in their balance sheet
composition. To facilitate the theoretical analysis of
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28
Table 8. The evolution of the fiscal multipliers1999 2001 2003
2005 2007 2009 2011 2013
∆yt∆gt 1.69 1.71 1.70 1.79 1.85 2.22 2.26 2.37∆ct∆gt 0.90 0.93
0.92 1.03 1.11 1.57 1.61 1.75
the effect of wealth on consumption, we abstract from
differences in labor income. Thecategories of households that we
consider match some of the most popular ones in theliterature along
with some others that have attracted much attention recently:
Ricardians,rule-of-thumbers, mortgagors with high or low capacity
of borrowing, hand-to-moutherswith illiquid wealth (real state) but
no liabilities, and Eggertsson-Krugman consumers,who can borrow but
have not real state to collateralize their debt that has to be
guaranteedwith expected future income.
We have studied several issues related to the economy’s response
to fiscal shocksunder different assumptions concerning the
structure of individual balance sheets in theeconomy. Then we have
taken a closer look at the some of the most salient features ofthis
structure for the US economy, using the Panel Study of Income
Dynamics (PSID). Weconclude that while the distribution of
households is fairly stable for most of the types,the share of
Ricardians significantly declines during the Great Recession and
its aftermathwhile the share of Eggertsson-Krugman consumers
increases. Given that the consumptionresponse to a fiscal shock by
Eggertsson-Krugman consumers is the largest, our estimatessuggest
that the fiscal multiplier grows more than 30% between 2005 and
2013.
We show that matching stylised facts regarding households
finances is key to un-derstand the reaction of economies to fiscal
shocks. There are a number of relevant con-clusions that can be
drawn from our analysis. First, the marginal propensity to
consumeis negatively related with the net worth. Second, the size
of the fiscal effect is positivelycorrelated with ex ante wealth
inequality. Third, changing the composition of the popu-lation
importantly affects the aggregate marginal propensity to consume
and the outputmultiplier. Fourth, fiscal shocks have non negligible
distributional effects that are reflectednot only in size but also
in the sign of welfare changes for different segments of
thepopulation.
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29
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Appendix 1: The complete model
A.1 Households’ problems equations
First order conditions:
λi1t =1cit
i = {R, HNH, HH, BL, BH, EK} (1.1)
λR2tλR1t
= βREtλR1t+1
λR1t
{rt+1 + δ+
φ
2jR2t+1kR2t
+λR2t+1
λR1t+1(1− δ)
}(1.2)
λR2t = λR1t
[1+ φ
(jRt
kRt−1
)](1.3)
λR1t = βREtλR1t+1
{1+ rnt
1+ πt+1
}(1.4)
λi1t = βiEtλi1t+1
(1+ rnt
1+ πt+1
)+ µit (1+ r
nt ) i = {BL, BH, EK} (1.5)
λR1tqt =φRxxRt+ βREtqt+1λR1t+1 (1.6)
λi1tqt =φixxit+ µitm
iEtqt+1(1+ πt+1) + βiEtqt+1λi1t+1 i = {BL, BH} (1.7)
λHH1t qt =φHHxxHHt
+ βHHEtqt+1λHH1t+1 (1.8)
λiht = λi1twtl1t +
(φ1(1− l1t)1−η
1− η − φ2(1− l2)1−η
1− η
)(1.9)
+(1− σ− ρwt )βiEtλiht+1 i = {R, HNH, HH, BL, BH, EK}
-
32
Constraints:
cit+ qt(
xit − xit−1)= −(1+ rnt−1)
(bit−1
1+ πt
)+wtnit−1l1+ b
it+ trht i = {BL, BH, EK}
(1.10)
cHNHt = wtnHNHt−1 l1 + trht (1.11)
cHHt + qt(
xHHt − xHHt−1)= wtnHHt−1 l1 + trht (1.12)
bit ≤ miEt
(qt+1 (1+ πt+1) xit
1+ rnt
)i = {BL, BH} (1.13)
bEKt ≤[
mEKEt
((1+ πt+1)wt+1nEKt l1t+1
1+ rnt
)](1.14)
kRt = jRt + (1− δ)kRt−1 (1.15)
nit = (1− σ)nit−1 + ρwt (1− nit−1) (1.16)= (1− σ)nit−1 + χ1v
χ2t [(1− nt−1) l2]
1−χ2 i = {R, HNH, HH, BL, BH, EK}
A.2 Aggregation
ct = τRcRt + τHNHcHNHt + τ
HHcHHt + τBLcBLt + τ
BHcBHt + τEKcEKt (1.17)
nt = τRnRt + τHNHnHNHt + τ
HHnHHt + τBLnBLt + τ
BHnBHt + τEKnEKt (1.18)
τBLbBLt + τBHbBHt + τ
EKbEKt + τRbRt = 0 (1.19)
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33
τHHxHHt + τBLxBLt + τ
BHxBHt + τRxRt = X (1.20)
kt = τRkRt (1.21)
jt = τR jRt (1.22)
dt = −τRdRt (1.23)
A.3 Firms
πt = γf Etπt+1 + $m̂ct + γbπt−1 (1.24)
mct = mc(1+ m̂ct) (1.25)
rt = (1− α)mctyt
kt−1(1.26)
yt = Ak1−αt−1 (nt−1l1t)α (1.27)
λ f t = αmctyt
nt−1− wtl1t + (1− σ)βREt
λR1t+1
λR1tλ f t+1 (1.28)
κvvt = ρft vtβ
REtλR1t+1
λR1tλ f t+1
= χ1vχ2t [(1− nt−1) l2]
1−χ2 βREtλR1t+1
λR1tλ f t+1 (1.29)
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34
ρft =
χ1vχ2t [(1− nt−1) l2]
1−χ2
vt(1.30)
A.4 Bargaining in the labour market
wtl1t = λw(
αmctyt
nt−1+
κvvt(1− nt−1)
)+(1− λw)
[(τR
λR1t+
τHNH
λHNH1t+
τHH
λHH1t+
τBL
λBL1t+
τBH
λBH1t+
τEK
λEK1t
)(φ2(1− l2)1−η
1− η − φ1(1− l1t)1−η
1− η
)]
+(1− λw)(1− σ− ρwt )τHNHEtλHNHht+1
λHNH1t+1
(βR
λR1t+1
λR1t− βHNH λ
HNH1t+1
λHNH1t
)
+(1− λw)(1− σ− ρwt )τHHEtλHHht+1
λHH1t+1
(βR
λR1t+1
λR1t− βHH λ
HH1t+1
λHH1t
)
+(1− λw)(1− σ− ρwt )τBLEtλBLht+1
λBL1t+1
(βR
λR1t+1
λR1t− βBL λ
BL1t+1
λBL1t
)
+(1− λw)(1− σ− ρwt )τBHEtλBHht+1
λBH1t+1
(βR
λR1t+1
λR1t− βBH λ
BH1t+1
λBH1t
)
+(1− λw)(1− σ− ρwt )τEKEtλEKht+1
λEK1t+1
(βR
λR1t+1
λR1t− βEK λ
EK1t+1
λEK1t
)(1.31)
αmctyt
nt−1l1,t=
[τR
λR1t+
τHNH
λHNH1t+
τHH
λHH1t+
τBL
λBL1t+
τBH
λBH1t+
τEK
λEK1t
]φ1(1− l1t)−η (1.31)
ρwt =χ1v
χ2t [(1− nt−1) l2]
1−χ2
(1− nt−1)
A.5 Policy instruments and resources constraint
yt = ct + jt
(1+
φ
2
(jt
kt−1
))+ gt + κvvt (1.32)
-
35
1+ rnt =(1+ rnt−1
)rR ((1+ πt)1+rπ (yty)ry
(1+ rn))1−rR
(1.33)
dt = gt + trht +(1+ rnt−1)
1+ πtdt−1 (1.34)
trht = trht−1 − ψ1
[btyt−(
by
)]− ψ2
[btyt− bt−1
yt−1
](1.35)
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36
Appendix 2: Income and wealth in the PSID
INCOME
Income of a household contains the following categories:
• Salary• Dividends• Rent payments received• Worker comp• Trust
fund income• Financial support from relatives• Financial support
from non-relatives• Child Support Recieved• Alimony Recieved•
Supplemental security income, temp assistance for needy families
(state program),
Other welfare
• Pensions/annuity• Lump Sum Payments∗ Inheritances, itemized
deductions
• Financial Support given to others
WEALTH
Variable Wealth1 in the PSID includes
• Net value of farm or business assets• Value of checking
accounts, saving accounts, money market funds, certificates of
de-
posit, savings bonds, Treasury Bills, other IRAS.
• Value of debts other than mortgages (credit cards, student
loans, medical or legal bills,personal loans).
• Net value of real estate other than main home.• Value of
shares of stock in publicly held corps, mutual funds or investment
trusts.• Net value of vehicle or other assets ’on wheels’.• Value
of other investment in trusts or estates, bond funds,